Diffusion

Diffusion is the net movement of particles, such as atoms, ions, or molecules, from a region of higher concentration to a region of lower concentration.

This process is driven by a gradient in Gibbs free energy or chemical potential. A gradient is a change in the value of a quantity, such as concentration, pressure, or temperature, over a distance. When the concentration of a substance changes over a distance, it is called a concentration gradient. Diffusion is a stochastic process, which means it is based on inherent randomness. Because of this randomness, diffusion can be used to model many real-life scenarios in fields like statistics, probability theory, and even finance.

The mechanism of diffusion relies on a particle random walk.

In molecular diffusion, molecules in a gas, liquid, or solid are self-propelled by their own kinetic energy. These particles do not move in a straight line or a single direction. Instead, they move in a messy, irregular way, bumping into other particles. While there is no microscopic force pushing particles toward empty space, there is a statistical trend. Because there are more particles in high-concentration areas, the probability of them moving into low-concentration areas is higher. This results in mixing or mass transport without requiring any directed bulk motion. Bulk flow, or advection, is different because it involves the movement of an entire body due to a pressure gradient.

Scientists distinguish between different types of diffusion based on how they behave. If a process can be described by Fick's laws, it is called normal or Fickian diffusion. If it does not follow these laws, it is called anomalous or non-Fickian diffusion. In porous solids, the way particles move depends on the size of the pores. Molecular diffusion occurs when particles collide with other molecules more often than with the pore walls. Knudsen diffusion happens when the pore diameter is similar to or smaller than the mean free path of the molecule. In this case, collisions with the pore walls become more likely. Finally, configurational diffusion occurs when the molecules are a comparable size to the pores, which significantly lowers the diffusivity.

The history of studying diffusion spans from ancient observations to modern physics. Long ago, Pliny the Elder described the cementation process used to produce steel. This involved carbon diffusion into iron. In 1827, Robert Brown discovered Brownian movement. He observed minute particles suspended in a liquid moving with rapid, irregular motion under an optical microscope.

Later, Albert Einstein developed the theory of Brownian motion and the atomistic background of diffusion. In the 1830s, Thomas Graham performed the first systematic experimental study of diffusion in gases. He discovered that different gases spontaneously mix rather than arranging themselves by density. His work helped James Clerk Maxwell derive the coefficient of diffusion for CO2 in the air in 1867.

We can see the importance of these concepts in human biology. Breathing is a perfect example of how bulk flow and diffusion work together.

First, the lungs expand, which increases the volume of the alveoli. This expansion causes a decrease in pressure, creating a pressure gradient. Air moves into the lungs through bulk flow until the pressures are equal. Once the air is in the alveoli, diffusion takes over. The air has a higher concentration of oxygen than the blood in the surrounding capillaries. Oxygen moves down its concentration gradient into the blood. Simultaneously, carbon dioxide moves from the blood into the alveoli to be exhaled.

Diffusion also plays a role in extreme environments like outer space. In astronomy, scientists use atomic diffusion to model the atmospheres of chemically peculiar stars. It is also a critical factor in understanding the surface composition and evolution of white dwarf stars.

In the digital world, diffusion has found a new use in artificial intelligence. Since 2015, researchers have used diffusion models, also known as generative models, to train machines. These models learn a diffusion process from a dataset. This allows the computer to generate new elements that are distributed similarly to the original data. This technique uses principles from non-equilibrium thermodynamics to sample highly complex probability distributions.

Because of its mathematical nature, diffusion connects many different fields of study. It is used in chemistry to understand fluid movement in solids and in biology to study how ions move through cell membranes.

In sociology and economics, the concept helps describe the diffusion of ideas, people, and price values. Whether it is the movement of a single molecule or the spread of information through a population, the underlying principle of spreading from high to low concentration remains the same. This simple movement helps explain how systems reach equilibrium and how matter and information move through our world.